摘要：Let v = vrer + vθeθ + v3e3 be a Leray-Hopf solution to the axially symmetric Navier-Stokes equations (ASNS) in R3 × [0,T). We call it a partial type I solution if vr(x,t) ≥ −C/√T − t for some constant C > 0 and all (x,t) ∈ R3 × [0,T). In this paper, we prove that such a solu tion does not blow up at time T under the extra mild assumption that |vθ(x, 0)||x′| is bounded. This extends a well-known result established by two groups of authors, who proved the no-blowup conclusion under the full type I condition |v(x,t)| ≤ C/√T − t. Our result also confirms the physical intuition that potential blowups for the axially symmetric Navier-Stokes equations are caused by the supercritical inward radial velocity